TOOL 06 / SOLVERS

Matrices and simultaneous equations, row operation by row operation.

Type a matrix or a set of equations and get the answer with every step shown. On the second tab, solve differential equations and see the solution drawn.

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The Slide Rule matrix solver solving three simultaneous equations, with the working panel showing the augmented matrix and the row operations — Three equations in three unknowns. The working lines up the unknowns, writes the augmented matrix and eliminates with row operations.

WHAT IT DOES

Linear algebra you can follow.

The answers a matrix calculator gives, with the working your lecturer expects to see beside them.

Matrices as a grid

Fill in a grid, or type [1, 2; 3, 4] and it is built for you. Add, subtract and multiply as written; ^-1 is the inverse and ^2 the square.

The usual operations

Inverse, transpose, determinant, reduced row echelon form, rank, trace, eigenvalues and powers, each one key.

Simultaneous equations

Enter a system one equation per line, or type x + y = 3; x − y = 1. The solution comes with a check that it satisfies every equation.

Step-by-step working

Show working sets out the row operations, the cofactor expansion of a determinant and each entry of a product, one step at a time.

Vectors

Dot and cross products, the length of a vector and the angle between two.

Exact fractions

Whole-number matrices give exact answers: the inverse of [2, 1; 1, 3] has entries 3/5, −1/5, −1/5 and 2/5, not rounded decimals.

TRY THESE

The built-in examples.

Each is one click under “Try one” in the solver, and each has working to open.

YOU ENTERSLIDE RULE ANSWERSTHE WORKING SHOWS
2x + y − z = 8; −3x − y + 2z = −11; −2x + y + 2z = −3x = 2, y = 3, z = −1The augmented matrix, each row operation, then a check.
det [4, −2, 1; 3, 6, −4; 2, 1, 8]263How the determinant is found.
[2, 1; 1, 3]⁻¹[3/5, −1/5; −1/5, 2/5]How the inverse is found, in exact fractions.
[1, 2; 3, 4] × [5, 6; 7, 8][19, 22; 43, 50]Each entry of the product, row times column.
eig [2, 1; 1, 2]1 and 3How the eigenvalues are found.
(1, 2, 3) × (4, 5, 6)(−3, 6, −3)The cross product, component by component.

THE SECOND TAB

Differential equations, solved and drawn.

Write one equation of first to fourth order, or a system of first-order equations, give the initial conditions and any parameters, and the solution is computed numerically and plotted as you type.

See it as a solution against time, a phase plane or a slope field, and read the value at any time. Ten examples are a click away: exponential decay, logistic growth, RC charging, damped and driven oscillators, the pendulum, Van der Pol, predator–prey, the SIR epidemic model and the Lorenz system.

Solutions are numerical, from an adaptive Runge–Kutta method (Dormand–Prince 5(4)). The solver gives values and graphs rather than a formula for y.

The Slide Rule differential equation solver plotting the decaying oscillation of a damped oscillator, with its equation, initial conditions and parameters on the left — A damped oscillator, y″ = −c·y′ − k·y, with c = 0.5 and k = 4.

QUESTIONS

Before you open it.

Does the matrix calculator show steps?

Yes. Press Show working for the row operations of a row reduction or a system, the expansion of a determinant, and each entry of a matrix product.

Can I paste a matrix from a spreadsheet?

Yes. Rows copied from a spreadsheet paste in as a matrix. A matrix stored under a letter, such as A, can be used in the calculator as well.

What kinds of differential equation does it solve?

Initial-value problems: a single equation up to fourth order, or a system, linear or not. It solves them numerically, so it handles equations with no neat formula for an answer, such as the pendulum or the Lorenz system.

Is it free?

Yes. Both solvers and their working are in the free plan, with no account needed. Exporting results as CSV is part of Pro.

One of eight tools that work together.

A value from one goes straight into another

NOTHING TO INSTALL

See every row operation.

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